What Slope-Intercept Form Means and How to Find It

Two Formats of Linear Functions

Standard Form: ax + by = c

Examples:

• 5x + 3y = 18
• -¾x + 4y = 0
• 29 = x + y

Slope intercept form: y = mx + b

Examples:

• y = 18 - 5x
• y = x
• ¼x + 3 = y

The primary difference between these two forms is y. In slope-intercept form — unlike standard form —y is isolated. If you're interested in graphing a linear function on paper or with a graphing calculator, you'll quickly learn that an isolated y contributes to a frustration-free math experience.

Slope intercept form gets straight to the point:

y = mx + b

• m represents the slope of a line
• b represents the y-intercept of a line
• x and y represent the ordered pairs throughout a line

Learn how to solve for y in linear equations with single and multiple step solving.

Single Step Solving

Example 1: One Step

Solve for y, when x + y = 10.

1. Subtract x from both sides of the equal sign.

• x + y - x = 10 - x
• 0 + y = 10 - x
• y = 10 - x

Note: 10 - x is not 9x. (Why? Review Combining Like Terms.)

Example 2: One Step

Write the following equation in slope intercept form:

-5x + y = 16

In other words, solve for y.

1. Add 5x to both sides of the equal sign.

• -5x + y + 5x = 16 + 5x
• 0 + y = 16 + 5x
• y = 16 + 5x

Multiple Step Solving

Example 3: Multiple Steps

Solve for y, when ½x + -y = 12

1. Rewrite -y as + -1y.

½x + -1y = 12

2. Subtract ½x from both sides of the equal sign.

• ½x + -1y - ½x = 12 - ½x
• 0 + -1y = 12 - ½x
• -1y = 12 - ½x
• -1y = 12 + - ½x

3. Divide everything by -1.

• -1y/-1 = 12/-1 + - ½x/-1
• y = -12 + ½x

Example 4: Multiple Steps

Solve for y when 8x + 5y = 40.

1. Subtract 8x from both sides of the equal sign.

• 8x + 5y - 8x = 40 - 8x
• 0 + 5y = 40 - 8x
• 5y = 40 - 8x

2. Rewrite -8x as + - 8x.

5y = 40 + - 8x

Hint: This is a proactive step toward correct signs. (Positive terms are positive; negative terms, negative.)

3. Divide everything by 5.

• 5y/5 = 40/5 + - 8x/5
• y = 8 + -8x/5

Edited by Anne Marie Helmenstine, Ph.D.